# Worksheet: Grouped Frequency Tables

In this worksheet, we will practice reading and interpreting frequency tables and tally charts and forming a frequency table for a given quantitative data set.

**Q13: **

The table of numbers shows the marks of 30 students in a mathematics exam.

25 | 37 | 31 | 39 | 26 | 23 | 27 | 31 | 20 | 33 |

35 | 37 | 23 | 37 | 21 | 33 | 24 | 27 | 36 | 27 |

32 | 26 | 30 | 37 | 25 | 31 | 32 | 21 | 28 | 32 |

Using this data, complete the frequency table.

Marks | 20–23 | 24–27 | 28–31 | 32–35 | 36– | Total |
---|---|---|---|---|---|---|

Frequency | 30 |

- A4, 7, 4, 3, 5
- B5, 8, 5, 6, 6
- C6, 8, 7, 4, 5
- D6, 9, 8, 7, 6
- E3, 7, 5, 8, 7

**Q14: **

The table of data shows the heights in centimeters of teachers at a school. Using a frequency table, find the number of teachers who are 175 cm or more.

179 | 169 | 193 | 171 | 163 | 186 | 178 | 173 |

167 | 166 | 195 | 156 | 163 | 190 | 171 | 195 |

156 | 186 | 187 | 159 | 172 | 169 | 184 | 195 |

159 | 168 | 179 | 155 | 178 | 162 | 174 | 167 |

193 | 177 | 159 | 179 | 162 | 189 | 163 | 182 |

181 | 167 | 189 | 173 | 187 | 159 | 170 | 186 |

**Q15: **

The table shows the number of days taken off work by 40 workers in a year. By constructing a frequency table or otherwise, calculate the number of workers who took 20 or more days off work.

16 | 18 | 5 | 20 | 15 | 26 | 12 | 17 | 8 | 5 |

5 | 12 | 26 | 30 | 23 | 22 | 21 | 30 | 25 | 21 |

27 | 15 | 12 | 28 | 11 | 12 | 26 | 12 | 13 | 23 |

6 | 29 | 28 | 5 | 20 | 12 | 10 | 24 | 23 | 14 |

**Q16: **

The table shows the weekly wages of 30 workers in a factory. By forming the frequency table using the intervals 30–39, 40–49, 50–59, 60–69, 70–79, 80–89, and 90–99, find which interval has the highest frequency.

43 | 47 | 43 | 99 | 54 | 47 | 53 | 100 | 46 | 97 |

50 | 41 | 36 | 72 | 38 | 37 | 80 | 46 | 74 | 74 |

30 | 34 | 32 | 97 | 90 | 35 | 68 | 87 | 78 | 30 |

- A60–69
- B50–59
- C40–49
- D30–39

**Q19: **

The table shows the marks of 100 students in a recent science exam. What percentage of students received 20 marks or more?

Mark | 0– | 10– | 20– | 30– | 40– | 50– | Total |
---|---|---|---|---|---|---|---|

Frequency | 5 | 25 | 21 | 16 | 19 | 14 | 100 |

**Q20: **

Given an interval with lower limit 16 and center 23, find the upper limit of the interval.

**Q21: **

The table shows donations made by students to a charity. How many students donated between 60–70 pounds?

Donation in Pounds | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70– | Total Number of Students |
---|---|---|---|---|---|---|---|

Number of Students | 4 | 2 | 3 | 7 | 16 | 5 | 37 |

**Q22: **

The table shows the distribution of exam marks in science for 1 000 students. By drawing a cumulative frequency curve, determine the number of students who scored 54 marks or more.

Scores | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | 80–89 | 90–99 | Total |
---|---|---|---|---|---|---|---|---|---|

Frequency | 105 | 134 | 124 | 130 | 119 | 156 | 110 | 122 | 1 000 |

- A637 students
- B585 students
- C631 students
- D124 students
- E507 students

**Q23: **

The table shows the bonuses received by 75 factory workers. How many workers received a bonus which was less than 50 LE?

Bonus (LE) | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70– | Total |
---|---|---|---|---|---|---|---|

Number of Workers | 10 | 5 | 10 | 15 | 25 | 10 | 75 |

**Q24: **

The scores that 30 students achieved in a maths exam are shown in the table. By constructing a frequency table of the scores, with groups 20–23, 24–27, 28–31, 32–35, and 36–39, find the group with the lowest frequency.

28 | 30 | 39 | 37 | 36 | 28 | 28 | 35 | 33 | 25 |

39 | 39 | 27 | 20 | 39 | 31 | 36 | 28 | 20 | 35 |

32 | 37 | 38 | 30 | 31 | 25 | 29 | 28 | 39 | 36 |

- A32–35
- B20–23
- C24–27
- D28–31
- E36–39

**Q25: **

The table shows the marks of 100 students in a recent mathematics exam. What percentage of students received 30 marks or more?

Marks | 0–9 | 10–19 | 20–29 | 30–39 | 40–49 | 50–59 | Total |
---|---|---|---|---|---|---|---|

Frequency | 8 | 22 | 15 | 22 | 16 | 17 | 100 |